Question

The size of the image formed by a convex mirror of focal length 30 cm is a quarter of the size of a real object. Then the distance of the object from the mirror is

Answer 1

Given, H_i = H_o/4 and f = 30 cm
As, magnification is given by :
$m=\frac{heightofimage}{heightofobject}=\frac{H_0/4}{H_0}=\frac{1}{4}$ .........(1)
As, m = $\frac{imagedis\tan ce}{objectdis\tan ce}=-\frac{v}{u}$ = $\frac{1}{4}$ ...............(2)
so, u = -4v
as, mirror formula is given by :
$\frac{1}{f}=\frac{1}{u}+\frac{1}{v}$ ............(3)
put value of u in eq (3), to know the object distance from the mirror.